DotaMath: Decomposition of Thought with Code Assistance and Self-correction for Mathematical Reasoning

TL;DR

DotaMath introduces a decomposition-based approach with code assistance and self-correction for complex mathematical reasoning in large language models, significantly improving performance on challenging benchmarks.

Contribution

The paper presents DotaMath, a novel framework that decomposes complex math problems, uses code for solutions, and incorporates self-correction, along with a large fine-tuning dataset and competitive results.

Findings

DotaMath models achieve 64.8% on MATH dataset.

DotaMath models reach 86.7% on GSM8K.

The approach outperforms open-source LLMs on various benchmarks.

Abstract

Large language models (LLMs) have made impressive progress in handling simple math problems, yet they still struggle with more challenging and complex mathematical tasks. In this paper, we introduce a series of LLMs that employs the Decomposition of thought with code assistance and self-correction for mathematical reasoning, dubbed as DotaMath. DotaMath models tackle complex mathematical tasks by decomposing them into simpler logical subtasks, leveraging code to solve these subtasks, obtaining fine-grained feedback from the code interpreter, and engaging in self-reflection and correction. By annotating diverse interactive tool-use trajectories and employing query evolution on GSM8K and MATH datasets, we generate an instruction fine-tuning dataset called DotaMathQA with 574K query-response pairs. We train a series of base LLMs using imitation learning on DotaMathQA, resulting in DotaMath models that achieve remarkable performance compared to open-source LLMs across various in-domain and out-of-domain benchmarks. Notably, DotaMath-deepseek-7B showcases an outstanding performance of 64.8% on the competitive MATH dataset and 86.7% on GSM8K. Besides, DotaMath-deepseek-7B maintains strong competitiveness on a series of in-domain and out-of-domain benchmarks (Avg. 80.1%). Looking forward, we anticipate that the DotaMath paradigm will open new pathways for addressing intricate mathematical problems. Our code is publicly available at https://github.com/ChengpengLi1003/DotaMath.